This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Proceedings of the London Mathematical Society following peer review. The definitive publisher-authenticated version "Equivariant Flow Equivalence for Shifts of Finite Type, by Matrix Equivalence Over Group Rings," Proceedings of the London Mathematical Society, 91(1):184-214, is available online at:


Let G be a finite group. We classify G-equivariant flow equivalence of non-trivial irreducible shifts of finite type in terms of

(i) elementary equivalence of matrices over ZG and

(ii) the conjugacy class in ZG of the group of G-weights of cycles based at a fixed vertex.

In the case G = Z/2, we have the classification for twistwise flow equivalence. We include some algebraic results and examples related to the determination of E(ZG) equivalence, which involves K1(ZG). (444 kB)
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